Problem: Graph this system of equations and solve. $3x-4y = 20$ $-6x-4y = -16$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Convert the first equation, $3x-4y = 20$ , to slope-intercept form. $y = \dfrac{3}{4} x - 5$ The y-intercept for the first equation is $-5$ , so the first line must pass through the point $(0, -5)$ The slope for the first equation is $\dfrac{3}{4}$ . Remember that the slope tells you rise over run. So in this case for every $3$ positions you move up You must also move $4$ positions to the right. $4$ positions to the right. $3$ positions up from $(0, -5)$ is $(4, -2)$ Graph the blue line so it passes through $(0, -5)$ and $(4, -2)$ Convert the second equation, $-6x-4y = -16$ , to slope-intercept form. $y = -\dfrac{3}{2} x + 4$ The y-intercept for the second equation is $4$ , so the second line must pass through the point $(0, 4)$ The slope for the second equation is $-\dfrac{3}{2}$ . Remember that the slope tells you rise over run. So in this case for every $3$ positions you move down (because it's negative) You must also move $2$ positions to the right. $2$ positions to the right. $3$ positions down from $(0, 4)$ is $(2, 1)$ Graph the green line so it passes through $(0, 4)$ and $(2, 1)$ The solution is the point where the two lines intersect. The lines intersect at $(4, -2)$.